"Throughout the "Cold War" the USA had a significant lead over the USSR as far as nuclear bombs were concerned. So thinking at it from that point of view, the USA could have dealt a lot more damage to the USSR."
No offence but thats not all of the story. USA did NOT always have a lead in "bombs" (missiles were the real players in cold war), and nor they do today. The USSR was the first nation to make a practical H bomb (one that actually fits inside an aircraft bomb-bay instead of something the size of a house which isnt a use at all. They also created BY FAR the most powerful weapon in history, Tzar bomba had a yield of 50MT, (most powerful nuclear weapon USA ever had in terms of yield was 15MT).
USSR was the first to introduce ICBMs with the R-7 semyorka, it was for some time light years ahead from anything US possessed. Manned bombers of which USAF Stratifical Air Command had better advantage over its soviet counterparts at that particular time soon became irrelevant. However US did take a lead few years later when they introduced there own ICBM that were much lighter and more compact then there soviet counterparts. from 1945 to 1965, USA did have a slight edge over USSR in total nuclear strike capability, but later on Soviets to turn that over by developing monstrously powerful and sophisticated weapon systems that some still have no counterpart today such as the R-36, TOPOL-M ICBMs, Even Russia today IMO has an edge in first strike nuclear capability.
USA did initially have a lead in developing smaller and more compact (and hence more practical) SLBMs (submarine lunched ballistic missiles) with missiles such as the Polaris, But that lead was turned around with newer soviet missiles such as the R-29.
Soviets also had a much more organised and planned evacuation plan and understructure than USA did. If you go to any big cities in Russia or other post soviet states, you can find massive networks of underground bunkers designed to hold vast amount of people for long peroids, some even had nuclear power stations to keep them running for long periods from the outside nuclear winter. USA had no such things, it had plans to look after the 10% of the populations elites, namely the political and economical elites, they never went to the trouble of investing and planning such defensive measures for its population. Soviets were probably more concious after loosing 22-28 million lives in WW2.
These are all theoretical. The real outcome of the cold war turning hot is beyond anyone's comprehension, i love to see wise asses (not you personally but everyone in this thread, including me time to time :P) make predictions on such things. From what military histories tell us, predictions whether there made by "experts", Generals, politicians or Historians turn out to be completely wrong 99/100 of times. Who would have predicted WW1 would end up being a bloody stalemate? Who would have guessed of the combined arms operation that the Germans exploited ruthlessly at the beginning of WW2 as it took over europe, so called experts were still getting there head around WW1 tactics and strategy (certainly the french and English military though that way at the time). Vietnam apparently ment to be a walk in the park but outcomes always turn different.
True story isNo one knows what the outcome would be, there would be massive lives lost on both sides and no one would want to count who lost more. It is impossible to guess the outcomes and nature of such conflicts unless it already occurred. Warfare is one of the most unpredictable things to study